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Like AR, MA models essentially need the series to be stationary, do the other forecast methods mentioned above also follow stationary?

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I would not classify all of those things as "methods", at least not in the same sense as AR and MA. A Naive forecast could be done in many ways; it is a principle, that forecast accuracy shouldn't be evaluated in a vacuum but rather should be evaluated within a forecast value added framework, comparing each forecasting step back to a "naive approach" and ensuring that the increase in accuracy (if any) is worth the time/energy/money it costs to create the forecast.

As @Nishad's link indicates there are forecasting methods that can be used with non-stationary data; therefore, one should utilize a naive forecast. The phrases in your question are all things that might be done as a naive forecast. If the data is not stationary, this might inform your choice of what makes a suitable naive forecast (it shouldn't be "too naive"-- what's the best easy forecast to produce).

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